Computational Procedure Based on the Block Gauss-Seidel Algorithm

Previous Calculation Procedure

In [23], a calculation procedure to solve the equation (5-36) has been proposed:

  • 1. First, the fundamental harmonic A1 is calculated based on the assumption of setting A2 to An to zero. If the convergence of A1 is satisfied, turn to step 2. If not, update A1 and repeat step 1.
  • 2. The other harmonics, A2 to AN, are calculated respectively with the known A1. If the convergence of A2 to AN is satisfied, the calculation procedure stops. If not, turn to step 1.

However, the computational procedure above is not dependable nor efficient. The convergent criterion in each harmonic computation and the lack of full use of updated solutions in nonlinear iterations leads to convergence uncertainty and the subsequent inaccuracy of harmonic solutions, especially when the nonlinearities of the magnetic material are strong. Yamada [23] also pointed out that there is convergence uncertainty in the iterative approach. In fact, a compulsory stop is usually done, by setting a maximum number of iterative steps.

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